Letters are not often the best way to start conversations like this with your employer. Unless you have already spoken to your boss and he or she had requested that you put this in writing, I would really recommend you TALK to your boss about this. In the US, no one gets a one-month paid leave for a reason like this, so this is an odd request for me. Is it even allowed within the terms of your employment? That's another reason to talk to someone first. I would say "For family reasons," however, "to spend time with my boyfriend."